Some defenders of the view that there is a common morality have conceived such morality as being universal, in the sense of extending across all cultures and times. Those who deny the existence of such a common morality often argue that the universality claim is implausible. Defense of common morality must take account of the distinction between descriptive and normative claims that there is a common morality. This essay considers these claims separately and identifies the nature of the arguments for each claim. It argues that the claim that there is a universal common morality in the descriptive sense has not been successfully defended to date. It maintains that the claim that there is a common morality in the normative sense need not be understood as universalist. This paper advocates the concept of group specific common morality, including country-specific versions. It suggests that both the descriptive and the normative claims that there are country-specific common moralities are plausible, and that a country-specific normative common morality could provide the basis for a country's bioethics.